Crocheting Bour's $\mathcal{B}_m$ minimal surfaces

Abstract: Minimal surfaces can be though as a mathematical generalisation of surfaces formed by soap films. We consider Bour's minimal surfaces $\mathcal{B}_m$ that are intrinsically surfaces of revolution. We show how to generate crochet patterns for $\mathcal{B}_m$ surfaces using basic trigonometric identities to calculate required arc lengths. Three special cases of $\mathcal{B}_m$ surfaces are considered in more detail, namely Enneper's, Richmond's, and Bour's $\mathcal{B}_3$ surfaces, and we provide exact crochet instructions for the classical Enneper's surface.